Scale-dependent non-gaussianities in the CMB data identified with Minkowski functionals and scaling indices

Abstract

We present further investigations of the Wilkinson Microwave Anisotropy Probe (WMAP) data by means of the Minkowski functionalsand the scaling index method. In order to test for non-Gaussianities (NGs) with respect to scale dependences, we use the so-called surrogate maps, in which possible phase correlations of the Fourier phases of the original WMAP data and the simulations, respectively, are destroyed by applying a shuffling scheme to the maps. A statistical comparison of the original maps with the surrogate maps then allows us to test for the existence of higher order correlations (HOCs) in the original maps, also and especially on well-defined Fourier modes. We calculate the Σ-normalized deviation between the Minkowski functionals of original data and 500 surrogates for different hemispheres in the sky and find ecliptic hemispherical asymmetries between the northern and southern ecliptic sky. Using Minkowski functionals as an image analysis technique sensitive to HOCs, we find deviations from Gaussianity in the WMAP data with an empirical probability p > 99.8 per cent when considering the low l-range with δ l = [2, 20]. The analysis technique of the scaling indices leads to the same results for this l-interval with a slightly lower deviation but still at p > 99.8 per cent. Although the underlying foreground reduction methods of the maps differ from each other, we find similar results for the WMAP seven-year internallinear combination map and the WMAP seven-year needlet-based ILC map for deviations from Gaussianity in the low l-range. Our results point once more to a cosmological nature of the signal. For a higher l-range with δ l = [120, 300], the results differ between the two image analysis techniques and between the two maps which makes an intrinsic nature of the signal on this l-range less likely. When we decrease the size of the analysed sky regions for the low-l study, we do not find signatures of NG in the northern ecliptic sky. In the south, we find individual spots which show deviations from Gaussianity. In addition, we investigate non-Gaussian cosmicmicrowave background simulations that depend on the fNL parameter of the local type. These simulations with flocalNL = [0,±100,±1000] cannot account for the detected signatures on the low l-range. © 2012 The Authors.